News recommendation aims to help online news platform users find their preferred news articles. Existing news recommendation methods usually learn models from historical user behaviors on news. However, these behaviors are usually biased on news providers. Models trained on biased user data may capture and even amplify the biases on news providers, and are unfair for some minority news providers. In this paper, we propose a provider fairness-aware news recommendation framework (named ProFairRec), which can learn news recommendation models fair for different news providers from biased user data. The core idea of ProFairRec is to learn provider-fair news representations and provider-fair user representations to achieve provider fairness. To learn provider-fair representations from biased data, we employ provider-biased representations to inherit provider bias from data. Provider-fair and -biased news representations are learned from news content and provider IDs respectively, which are further aggregated to build fair and biased user representations based on user click history. All of these representations are used in model training while only fair representations are used for user-news matching to achieve fair news recommendation. Besides, we propose an adversarial learning task on news provider discrimination to prevent provider-fair news representation from encoding provider bias. We also propose an orthogonal regularization on provider-fair and -biased representations to better reduce provider bias in provider-fair representations. Moreover, ProFairRec is a general framework and can be applied to different news recommendation methods. Extensive experiments on a public dataset verify that our ProFairRec approach can effectively improve the provider fairness of many existing methods and meanwhile maintain their recommendation accuracy.